Question

The number of database queries made during any interval of time is a Poisson random variable. On average, six queries are made every minute. Determine the probability that three or more queries will be made during an interval of 15 seconds.

Answer #1

Solution :

Given that ,

mean = = 6

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

P(X 3) = 1 - P(X 2 )

= 1 - ( P(X = 0) + P(X = 1) + P(X = 2))

= 1 - ( (e^{6} * 6^{0}) / 0! +
(e^{6} * 6^{1}) / 1! + (e^{6} *
6^{2}) / 2!

= 1 - (0.0025+0.0149+0.0446)

= 1 - 0.0620

= **0.9380**

**The probability that three or more queries will be made
during an interval of 15 seconds is 0.9380.**

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